hnlmix: Generalized Nonlinear Regression using h-likelihood for a Random Parameter

Description

hnlmix fits user-specified nonlinear regression equations to one or both parameters of the common one and two parameter distributions. One parameter of the location regression is random with some specified mixing distribution.

Usage

hnlmix(
  y = NULL,
  distribution = "normal",
  mixture = "normal",
  random = NULL,
  nest = NULL,
  mu = NULL,
  shape = NULL,
  linear = NULL,
  pmu = NULL,
  pshape = NULL,
  pmix = NULL,
  prandom = NULL,
  delta = 1,
  common = FALSE,
  envir = parent.frame(),
  print.level = 0,
  typsize = abs(p),
  ndigit = 10,
  gradtol = 1e-05,
  stepmax = 10 * sqrt(p %*% p),
  steptol = 1e-05,
  iterlim = 100,
  fscale = 1,
  eps = 1e-04,
  points = 5
)

Value

A list of class hnlmix is returned that contains all of the relevant information calculated, including error codes.

The two variances and shrinkage estimates of the random effects are provided.

Arguments

y: A response vector of uncensored data, a two column matrix for binomial data or censored data, with the second column being the censoring indicator (1: uncensored, 0: right censored, -1: left censored), or an object of class, response (created by restovec) or repeated (created by rmna or lvna). If the repeated data object contains more than one response variable, give that object in envir and give the name of the response variable to be used here.
distribution: The distribution for the response: binomial, beta binomial, double binomial, mult(iplicative) binomial, Poisson, negative binomial, double Poisson, mult(iplicative) Poisson, gamma count, Consul generalized Poisson, logarithmic series, geometric, normal, inverse Gauss, logistic, exponential, gamma, Weibull, extreme value, Cauchy, Pareto, Laplace, Levy, beta, simplex, or two-sided power. (For definitions of distributions, see the corresponding [dpqr]distribution help.)
mixture: The mixing distribution for the random parameter (whose initial values are supplied in prandom): normal, logistic, inverse Gauss, gamma, inverse gamma, Weibull, or beta. The first two have zero location parameter, the next three have unit location parameter, and the last one has location parameter set to 0.5.
random: The name of the random parameter in the mu formula.
nest: The cluster variable classifying observations by the unit upon which they were observed. Ignored if y or envir has class, response or repeated.
mu: A user-specified formula containing named unknown parameters, giving the regression equation for the location parameter. This may contain the keyword, linear referring to a linear part.
shape: A user-specified formula containing named unknown parameters, giving the regression equation for the shape parameter. This may contain the keyword, linear referring to a linear part. If nothing is supplied, this parameter is taken to be constant. This parameter is the logarithm of the usual one.
linear: A formula beginning with ~ in W&R notation, specifying the linear part of the regression function for the location parameter or list of two such expressions for the location and/or shape parameters.
pmu: Vector of initial estimates for the location parameters. These must be supplied either in their order of appearance in the formula or in a named list.
pshape: Vector of initial estimates for the shape parameters. These must be supplied either in their order of appearance in the expression or in a named list.
pmix: If NULL, this parameter is estimated from the variances. If a value is given, it is taken as fixed.
prandom: Either one estimate of the random effects or one for each cluster (see nest), in which case the last value is not used. If the location parameter of the mixing distribution is zero, the last value is recalculated so that their sum is zero; if it is unity, they must all be positive and the last value is recalculated so that the sum of their logarithms is zero; if it is 0.5, they must all lie in (0,1) and the last value is recalculated so that the sum of their logits is zero.
delta: Scalar or vector giving the unit of measurement (always one for discrete data) for each response value, set to unity by default. For example, if a response is measured to two decimals, delta=0.01. If the response is transformed, this must be multiplied by the Jacobian. The transformation cannot contain unknown parameters. For example, with a log transformation, delta=1/y. (The delta values for the censored response are ignored.)
common: If TRUE, the formulae with unknowns for the location and shape have names in common. All parameter estimates must be supplied in pmu.
envir: Environment in which model formulae are to be interpreted or a data object of class, repeated, tccov, or tvcov; the name of the response variable should be given in y. If y has class repeated, it is used as the environment.
print.level: Arguments for nlm.
typsize: Arguments for nlm.
ndigit: Arguments for nlm.
gradtol: Arguments for nlm.
stepmax: Arguments for nlm.
steptol: Arguments for nlm.
iterlim: Arguments for nlm.
fscale: Arguments for nlm.
eps: Arguments for nlm.
points: Arguments for nlm.

Author

J.K. Lindsey

Details

It is recommended that initial estimates for pmu and pshape be obtained from gnlr.

These nonlinear regression models must be supplied as formulae where parameters are unknowns. (See finterp.)

Examples

Run this code


dose <- c(9,12,4,9,11,10,2,11,12,9,9,9,4,9,11,9,14,7,9,8)
#y <- rgamma(20,2+0.3*dose,scale=2)+rep(rnorm(4,0,4),rep(5,4))
y <- c(8.674419, 11.506066, 11.386742, 27.414532, 12.135699,  4.359469,
       1.900681, 17.425948,  4.503345,  2.691792,  5.731100, 10.534971,
      11.220260,  6.968932,  4.094357, 16.393806, 14.656584,  8.786133,
      20.972267, 17.178012)
resp <- restovec(matrix(y, nrow=4, byrow=TRUE), name="y")
reps <- rmna(resp, tvcov=tvctomat(matrix(dose, nrow=4, byrow=TRUE), name="dose"))

# same linear normal model with random normal intercept fitted four ways
# compare with growth::elliptic(reps, model=~dose, preg=c(0,0.6), pre=4)
glmm(y~dose, nest=individuals, data=reps)
gnlmm(reps, mu=~dose, pmu=c(8.7,0.25), psh=3.5, psd=3)
hnlmix(reps, mu=~a+b*dose+rand, random="rand", pmu=c(8.7,0.25),
	pshape=3.44, prandom=0)

# gamma model with log link and random normal intercept fitted three ways
glmm(y~dose, family=Gamma(link=log), nest=individuals, data=reps, points=8)
gnlmm(reps, distribution="gamma", mu=~exp(a+b*dose), pmu=c(2,0.03),
	psh=1, psd=0.3)
hnlmix(reps, distribution="gamma", mu=~exp(a+b*dose+rand), random="rand",
	pmu=c(2,0.04), pshape=1, prandom=0)

# gamma model with log link and random gamma mixtures
hnlmix(reps, distribution="gamma", mixture="gamma",
	mu=~exp(a*rand+b*dose), random="rand", pmu=c(2,0.04),
	pshape=1.24, prandom=1)
hnlmix(reps, distribution="gamma", mixture="gamma",
	mu=~exp(a+b*dose)*rand, random="rand", pmu=c(2,0.04),
	pshape=1.24, prandom=1)

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